Logic (nested quantifiers)

[Miike012]

Can someone tell me if my statement is equivalent to the one in the paint document?

My statement:
x and y will define all people
P(x): "x is a parent"
F(x): "x is female"
M(x,y): " x is the mother of y"

My answer is boxed in the paint doc (SECOND POST)

 

[Miike012]

My answer
Sorry, for some reason when I was trying to edit me first post I was unable to add another pic

 

[verty]

The $\forall x$ has no effect because the next $\exists x$ covers the whole block, so we can drop the $\forall x$. Try changing $\forall x$ to $\forall z$ to see the effect that it is having on the statement. What name the variable has changes nothing.

So your statement means there is at least one person who is not female or not a parent or is someone's mother.

 

[Miike012]

The $\forall x$ has no effect because the next $\exists x$ covers the whole block, so we can drop the $\forall x$. Try changing $\forall x$ to $\forall z$ to see the effect that it is having on the statement. What name the variable has changes nothing.

So your statement means there is at least one person who is not female or not a parent or is someone's mother.

Ok thank you. could you take a look at two more?